A linear interpolator is provided that includes differential pairs of transistors biased such that a first input voltage may be multiplied by a factor r wherein 0≦r≦1 and such that a second input voltage may be multiplied by the complement factor (1−r). By combining the multiplied input voltages, a linear interpolation is provided based upon the factor r.
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1. A linear interpolator for interpolating a first input voltage vin1 and a second input voltage vin2 according to a factor r, wherein 0≦r≦1, comprising:
a first differential pair of transistors adapted to split a differential current proportional to vin1 such that a first transistor in the first differential pair conducts a differential current proportional to r*vin1 and a second transistor conducts a differential current proportional to (1−r)*vin1; and
a second differential pair of transistors adapted to split a current proportional to vin2 such that a first transistor in the second differential pair conducts a differential current proportional to (1−r)*vin2 and a second transistor in the second differential pair conducts a differential current proportional to r*vin2.
11. A linear interpolator for interpolating a first input voltage vin1 and a second input voltage vin2 according to a factor r, wherein 0≦r≦1, comprising:
a first differential pair adapted to split a differential current proportional to r2 such that a first transistor in the first differential pair conducts a differential current proportional to vin1*r and a second transistor in the first differential pair conducts a differential current proportional to −Vin1*r; and
a second differential pair adapted to split a differential current proportional to (1−r)2 such that a first transistor in the second differential pair conducts a differential current proportional to vin2*(1−r) and a second transistor in the second differential pair conducts a differential current proportional to −Vin2*(1−r).
2. The linear interpolator of
a third differential pair of transistors adapted to split a differential current proportional to −Vin1 such that a first transistor in the third differential pair conducts a differential current proportional to −r*vin1 and a second transistor in the third differential pair conducts a differential current proportional to (1−r)*vin1; and
a fourth differential pair of transistors adapted to split a differential current proportional to −Vin2 such that a first transistor in the fourth differential pair conducts a differential current proportional to −(1−r)*vin2 and a second transistor in the fourth differential pair conducts a current proportional to −r*vin2.
3. The linear interpolator of
4. The linear interpolator of
5. The linear interpolator of
a first load coupled between a supply voltage and the first transistors in the first and second differential pairs such that the differential currents conducted by the first transistors in the first and second differential pairs are supplied through the first load, thereby inducing a first voltage across the first load.
6. The linear interpolator of
a second load coupled between the supply voltage and the first transistors in the third and fourth differential pairs such that the differential currents conducted by the first transistors in the third and fourth differential pairs are supplied through the second load, thereby inducing a second voltage across the second resistor, and wherein the difference between the second and first voltages is proportional to r*vin1+(1−r)vin2.
7. The linear interpolator of
8. The linear interpolator of
9. The linear interpolator of
10. The linear interpolator of
12. The linear interpolator of
a first load coupled between a supply voltage and the first transistors in the first and second differential pairs such that the differential currents conducted by the first transistors in the first and second differential pairs are supplied through the first load, thereby inducing a first voltage across the first load.
13. The linear interpolator of
a second load coupled between the supply voltage and the second transistors in the first and second differential pairs such that the differential currents conducted by the second transistors in the first and second differential pairs are supplied through the second load, thereby inducing a second voltage across the second load, and wherein the difference between the second and first voltages is proportional to r*vin1+(1−r)vin2.
14. The linear interpolator of
a third differential pair adapted to split a current such that a first transistor in the third differential pair conducts a differential current proportional to r and a second transistor in the third differential pair conducts a differential current proportional to (1−r).
15. The linear interpolator of
16. The linear interpolator of
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This invention relates generally to the interpolation of analog signals, and more particularly to the linear interpolation of analog signals.
Interpolation of signals is widespread in fields such as image processing and communication. Accordingly, much effort has been expended in the development of methods and systems to perform the necessary interpolation. But this interpolation will generally occur digitally, i.e., either the desired amount of interpolation is a digital value and/or the signals being interpolated are digital signals. Surprisingly little development has occurred regarding the interpolation of analog signals.
This difference in the prior art between the development for interpolation of digital signals vs. the development for interpolation of analog signals is understandable given the widespread nature of digital systems. However, even in digital systems such as those used for digital communications, the need arises for interpolation of analog signals such as that which occurs in adaptive timing control and recovery schemes. Existing analog signal interpolators have proven to be inappropriate for use in these schemes because they typically provide non-linear interpolation that is subject to gain variation. However, linear interpolation is often required and is essential when implemented in adaptive timing control and recovery techniques.
Accordingly, there is a need in the art for improved techniques and devices for the linear interpolation of analog signals.
In accordance with one aspect of the invention, a linear interpolator for interpolating a first input voltage Vin1 and a second input voltage Vin2 according to a factor r, wherein 0≦r≦1 is provided. The interpolator includes a first differential pair of transistors adapted to split a differential current proportional to Vin1 such that a first transistor in the first differential pair conducts a differential current proportional to r*Vin1 and a second transistor conducts a differential current proportional to (1−r)*Vin1 and a second differential pair of transistors adapted to split a current proportional to Vin2 such that a first transistor in the second differential pair conducts a differential current proportional to (1−r)*Vin2 and a second transistor in the second differential pair conducts a differential current proportional to r*Vin2. Advantageously, a voltage generated from the sum of the differential currents proportional to r*Vin1 and (1−r)Vin2 produces the desired linear interpolation.
In accordance with another aspect of the invention, a linear interpolator for interpolating a first input voltage Vin1 and a second input voltage Vin2 according to a factor r, wherein 0≦r≦1 is provided. The linear interpolator includes a first differential pair adapted to split a current proportional to r2 such that a first transistor in the first differential pair conducts a differential current proportional to Vin1*r and a second transistor in the first differential pair conducts a differential current proportional to −Vin1*r; and a second differential pair adapted to split a current proportional to (1−r)2 such that a first transistor in the second differential pair conducts a differential current proportional to Vin2*(1−r) and a second transistor in the first differential pair conducts a differential current proportional to −Vin2*(1−r).
Referring now to
To provide the interpolation according to variable factor r, linear interpolator 100 exploits the current splitting property of differential pairs. For example, a differential pair 200 of matched NMOS transistors is shown in
r=½*[1+sqrt{m*(1−m/4)}] Eq (1)
where the factor m is given by
m=(Vr/ΔV)2 Eq. (2)
and where the factor ΔV is denoted as the overdrive voltage and equals the difference between Vgs and the transistors' 205 and 210 threshold voltage. As can be seen from equations (1) and (2), by proper selection of the splitting voltage Vr, the current splitting factor r may be arbitrarily varied in the range 0≦r≦1. The variation of the splitting factor r as a function of Vr/ΔV is shown in
The current splitting behavior of a differential pair as determined through equation (1) may be implemented in a linear interpolator in a number of fashions. For example,
Differential pair 401 supplies the current I to transistor M2 whereas differential pair 405 supplies the current I to transistor M3. Thus, current source 410 acts to bias transistors M4 and M5 in differential pair 401 with the same gate-to-source voltage (Vgs) analogously as discussed with respect to
Transistors M4 and M5 in differential pair 401 will thus each pass a current I/2 if input voltage Vin1 is zero. Similarly, transistors M6 and M7 in differential pair 405 will each pass a current I/2 if input voltage Vin2 is zero. As input voltages Vin1 and Vin2 are increased positively, more and more current will be steered to transistors M4 and M6, respectively. Using the transconductance gm for transistors M4 and M5, the current excited through each transistor in response to the input voltage Vin1 is given by (I/2+gm*Vin1/2) and (I/2−gm*Vin1/2), respectively. Similarly, the current excited through each transistor M6 and M7 in response to input voltage Vin2 is given by (I/2+gm*Vin2/2) and (I/2+gm*Vin2/2), respectively.
Since I/2 is a constant, the following discussion will ignore this current and consider only the currents induced by the input voltages Vin1 and Vin2. Since these input voltages are applied differentially, as used herein, the currents induced by the input voltages Vin1 and Vin2 shall be denoted as “differential currents.” In this regard, transistor M4 conducts a differential current of gm*Vin1/2 whereas transistor M5 conducts a differential current of −gm*Vin1/2. Similarly, transistor M6 conducts a differential current of gm*Vin2/2 whereas transistor M7 conducts a differential current of −gm*Vin2/2.
The respective differential currents through transistors M4, M5, M6, and M7 may be split as discussed with respect to
Differential pairs 425 and 430 split the differential currents corresponding to input voltage Vin2 in the same fashion. For example, differential pair 425 supplies the current conducted through transistor M6. The splitting voltage Vr (equaling Vr+−Vr−) is applied across transistors M12 and M13 in differential pair 425. Thus, differential current gm*Vin2/2 is split into a portion r*gm*Vin2/2 that passes through transistor M12 and a portion (1−r)*gm*Vin2/2 that passes through transistor M13. Similarly, differential pair 430 supplies the current conducted through transistor M7. The splitting voltage Vr is applied across transistors M15 and M14 in differential pair 430. Thus, differential current (−1)*gm*Vin2/2 is split into a portion −r*gm*Vin2/2 that passes through transistor M15 and a portion −(1−r)*gm*Vin2/2 that passes through transistor M14. Note the symmetry exhibited by the differential currents in the pair of differential pairs 415 and 420 and also in the pair of differential pairs 425 and 430. For example, the differential currents through transistors M11 and M10 are the opposites of the corresponding differential currents through transistors M8 and M9, respectively.
Having split the differential currents in this fashion, they may be combined as follows to produce the desired interpolation of input voltages Vin1 and Vin2. A node A supplies the currents to transistors M8 and M13. Thus, a current Iout+ through node A equals r*gm*Vin1/2+(1−r)*gm*Vin2/2. Similarly, a node D supplies the currents to transistors M11 and M14 so that a current Iout− through node D equals −(r*gm*Vin1/2+(1−r)*gm*Vin2/2). Each node A and D may couple to a supply voltage VCC through loads such as separate resistors of equal resistances R as shown in
Linear interpolator 500 in
A corresponding current (1−r)2I may be produced as follows. Transistor M17 in differential pair 501 provides a current (1−r)I to a differential pair 520 consisting of transistors M20 and M21. Transistor M21 receives differential voltage Vr− as its gate voltage such that it conducts the current (1−r)2I. Currents r2I and (1−r)2I are received at matched transistors M22 and M23. A pair of matched transistors M24 and M25 are coupled in a current-mirror configuration to matched transistors M22 and M23, respectively. Thus, transistor M24 will conduct a current equal or proportional to r2I, depending upon the matching between the transistors. Similarly, transistor M25 will conduct a current equal or proportional to (1−r)2I. A differential pair 525 consisting of transistors M26 and M27 provides the current to transistor M24. Similarly, a differential pair 530 consisting of transistors M28 and M29 provides the current to transistor M25. Thus, the transconductance for transistors M26 and M27 will be proportional to r whereas the transconductance for transistors M28 and M29 will be proportional to (1−r). Input voltage Vin1 is applied across transistors M26 and M27 such that the gate of transistor M26 receives differential input voltage Vin1+ whereas the gate of transistor M27 receives differential input voltage Vin1−. Similarly, input voltage Vin2 is applied across transistors M28 and M29 such that the gate of transistor M28 receives differential input voltage Vin2+ whereas the gate of transistor M29 receives differential input voltage Vin2−. In this fashion, transistors M26 and M27 conduct differential currents proportional to r*Vin1/2*I and −r*Vin1/2*I, respectively. Similarly, transistors M28 and M29 conduct differential currents proportional to (1−r)*Vin2/2*I and −(1−r)*Vin2/2*I, respectively. A node E supplies the currents to transistors M26 and M28. Similarly, a node F supplies the currents to transistors M27 and M29. Each node E and F may couple to VCC through identical resistors (not illustrated) having a resistance R in an analogous fashion discussed with respect to
Regardless of the topology used, it will be appreciated that linear interpolators in accordance with the present invention are configurable to provide a linear interpolation of input voltages Vin1 and Vin2 according to an arbitrary splitting factor r, where 0≦r≦1. In turn, this arbitrary splitting factor r is driven by the ratio between splitting voltage Vr and the overdrive voltage as discussed with respect to
Although the invention has been described with respect to particular embodiments, this description is only an example of the invention's application and should not be taken as a limitation. Consequently, the scope of the invention is set forth in the following claims.
Phanse, Abhijit, Mukherjee, Debanjan, Bhattacharjee, Jishnu
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